Introduction to energy problem - did I do this right?

[JSmithDawg]

Homework Statement

The bullet strikes a block of wood which exerts, on average, a force of 50,000N opposing the motion of the bullet. How far does the bullet penetrate?

Mass of bullet = 25g
Initial velocity of bullet = 350 m/s
Final velocity of bullet = 0 m/s

Homework Equations

Ei+work=Ef
K = ½mv^2
Energy = Force * Displacement

The Attempt at a Solution

Please excuse my attempt of it's egregiously wrong, I was just introduced to energy yesterday; this is one of the first problems I'm doing.

Anyways, because the final velocity of the bullet is zero, the bullet must have lost all of its energy, making Ef=0 J. The bullet initially had kinetic energy, making Ei=K. Thus, my new equation is
K+work = 0 J
½mv^2+work=0 J

I also know that the problem gave me how many Newtons oppose the object, but I need to find out how much energy it used. Since Energy = Force*Displacement, I can rewrite the equation as:
½mv^2+(F*Δx) = 0 J
So I solved it below...
½(.025kg)(350 m/s)^2+(-50000N*Δx) = 0 J
Δx=.03m

Did I do this problem right? If not, what did I do wrong?

 

[Chestermiller]

I didn't check your arithmetic, but you methodology is correct.

Chet

 

[haruspex]

It's the right answer according to what the questioner seems to expect you to do, but the question is actually wrong.
Knowing the average force you cannot deduce the distance, only the time. Your method effectively assumes a constant force. Average force is defined as $\Delta$momentum/$\Delta$time. In general, this gives a different number from $\Delta$KE/displacement.